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We analyse pp elastic scattering data at the highest accelerator energyregion (between 10 and 63 GeV) through a multiple diffraction approach. The useof Martin's formula in a model developed earlier is substituted by theintroduction of a complex elementary (parton-parton) amplitude. With this thetotal cross section and the real part of the hadronic amplitude may besimultaneously investigated and, with the exception of the diffraction minimumat some ISR energies, a satisfactory description of all experimental data isobtained. Total cross sections extrapolations to cosmic-ray energies (above 6TeV) show agreement with the reanalysis of the Akeno data performed by N. N.Nikolaev and also with Gaisser, Sukhatme and Yodh results, leading to theprediction 147 mb for the total cross section at 16 TeV. Physicalinterpretations and critical remarks concerning our parametrizations andresults are also presented and discussed.Comment: Text with 9 pages in LaTeX, 16 figures in PostScript. Submitted to  Physical Review

Multiple diffraction model for proton-proton elastic scattering and total cross section extrapolations to cosmic-ray energies